Theorem mobii 2063

Description: Formula-building rule for "at most one" quantifier (inference form). (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 17-Oct-2016.)

Hypothesis

Ref	Expression
mobii.1	⊢ (𝜓 ↔ 𝜒)

Assertion

Ref	Expression
mobii	⊢ (∃*𝑥𝜓 ↔ ∃*𝑥𝜒)

Proof of Theorem mobii

Step	Hyp	Ref	Expression
1		mobii.1	. . . 4 ⊢ (𝜓 ↔ 𝜒)
2	1	a1i 9	. . 3 ⊢ (⊤ → (𝜓 ↔ 𝜒))
3	2	mobidv 2062	. 2 ⊢ (⊤ → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒))
4	3	mptru 1362	1 ⊢ (∃*𝑥𝜓 ↔ ∃*𝑥𝜒)

Syntax hints:   ↔ wb 105  ⊤wtru 1354  ∃*wmo 2027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-eu 2029  df-mo 2030

This theorem is referenced by:  moaneu  2102  moanmo  2103  2moswapdc  2116  2exeu  2118  rmobiia  2666  rmov  2757  euxfr2dc  2922  rmoan  2937  2rmorex  2943  mosn  3628  dffun9  5245  funopab  5251  funco  5256  funcnv2  5276  funcnv  5277  fun2cnv  5280  fncnv  5282  imadif  5296  fnres  5332  ovi3  6010  oprabex3  6129  axaddf  7866  axmulf  7867  frecuzrdgtcl  10409  frecuzrdgfunlem  10416  fsum3  11390